HR: 1340h
AN: H23G-1710    [Abstracts]
TI: Global and local probability density function of non-reactive solute concentrations in heterogeneous porous formations
AU: Bellin, A
EM: alberto.bellin@unitn.it
AF: University of Trento, Dipartimento di Ingegneria Civile e Ambientale, via Mesiano 77, Trento, I-38050, Italy
AU: * Tonina, D
EM: dtonina@berkeley.edu
AF: University of California, Berkeley, Department of Earth and Planetary Science, 307 McCone Hall, Berkeley, CA 94720, United States
AB: Because of our inability to map the hydraulic properties of heterogeneous formations in detail, most models of solute transport treat solute concentrations as a stochastic variable usually providing only the ensemble mean and in same cases the concentration standard deviation. However, they all miss to give the local concentration probability density function (pdf), which describes the variability of solute concentrations entirely at a given location and is essential in risk analysis where confidence intervals and probability of exceeding threshold values are required. Therefore, we developed a new model for the pdf of the local concentration of conservative tracers migrating in heterogeneous aquifers. Our model accounts for dilution associated with pore scale dispersion, mechanical mixing within the sampling volume, and spreading due to formation heterogeneity. We modeled local concentration dynamics with an Ito Stochastic Differential Equation (SDE) that under the hypothesis of statistical stationarity leads to the Beta pdf for solute concentrations. This model is fully characterized by the solute concentration first two moments, which are the same pieces of information required for standard geostatistical techniques and predicted by stochastic solute transport models. Additionally, we show that in the absence of pore-scale dispersion and for point concentrations the pdf model converges to the binary distribution of Dagan [1982, Water Resour. Res. 18(4), 835-848], while it approaches the Normal distribution for sampling volumes much larger than the characteristic scale of the aquifer heterogeneity. Furthermore, accurate numerical simulations show that our model performs well regardless of aquifer heterogeneity and captures the smoothing effect of the sampling volume and the associated reduction of the probability of exceeding large concentrations. Moreover, we demonstrate that the same model with spatial moments of the solute concentration replacing the statistical moments can be applied to estimate the probability of exceeding a given concentration irrespective of the location within the plume providing a model of global uncertainty. Application of this model to point and vertically averaged bromide concentrations from the first Cape Cod tracer test and to a set of numerical simulations confirms the above findings and for the first time we demonstrate the superiority of the Beta model to both Normal and Log-Normal pdf in interpreting field data. Furthermore, we show that characterization of local concentrations as normally or log-normally distributed may result in severe underestimates of the probability of exceeding large concentrations.
DE: 1829 Groundwater hydrology
DE: 1832 Groundwater transport
DE: 1847 Modeling
DE: 1869 Stochastic hydrology
SC: Hydrology [H]
MN: 2007 Fall Meeting